Recording - December 2016 - 50

Figure 5 demonstrates per-frequency phase difference
between two mics spaced 1 foot (0.9 milliseconds)
away from each other. As you can see, higher frequencies exhibit progressively greater phase difference. This
is because the 1 foot of distance between the mics is
small compared to the wavelengths of low frequencies
(remember, 100 Hz is as long as a Mini Cooper).
For higher frequencies, 1 foot is a much bigger
percentage of wavelength. At 1000 Hz, which is 1.3
feet long, a 1-foot offset creates 318˚ of phase shift,
just shy of a complete wavelength. At 10000 Hz, a
very high frequency about a half-pinkie in length, 1
foot equates to an off-the-chart 3186˚ of phase difference, or about 9 wavelengths in length. Highs see
more shift than lows for the same distance offset.
Glancing at Figure 5, we see that 1,129 Hz is
360˚ offset in phase between the two microphones.
Rising in frequency, 2,257 Hz experiences 720˚ of
shift and 3,386 Hz is offset by 1080˚. These frequencies are each 360˚ apart in phase and all three mark
the beginning of another wave cycle. Since sine
waves are periodic, i.e. they repeat in shape every
360˚, we have two options when measuring phase
differences greater than one wavelength. The first
method is to measure infinitely upwards, as shown in
Figure 5. The second approach is to mark phase differences on a 0˚ to 360˚ scale, starting over at 0º for
every new cycle of a wave. When we compare relative phase between two sources (or two mics on one
source), this tells us all we need and keeps the numbers manageable. A phase difference of 90º sounds
the same as a phase difference of 90º + 360º, or
90º + 720º, etc. See Figure 6 for both possible numbering systems.
Phase interaction
So what happens when the two spaced piano mics
are mixed together in a console? Each frequency in the
sound experiences its own unique amount of cancellation or summation determined by its phase difference.
This is easiest to understand at the extremes. Two
waves 180˚ out of phase to each other are exact mirror opposites, and when mixed together their contrary positive and negative pressure changes cancel
each other out, rendering the frequency silent.
Oppositely, two waves 360˚ offset from each other
are identical in wave shape and thus sum together,
doubling in amplitude, and creating a +6 dB
increase in level for that frequency. Since all frequencies posses their own unique phase difference, each
experiences a unique amplitude change somewhere
between total cancellation and +6 dB summation.
Figure 7 demonstrates several key phase differences
and their associated amplitude changes.
Remember, every frequency has a unique phase
difference between our two spaced mics, so each frequency will have its own level change when the mics
are mixed together. From this we can make a bold
summarizing statement: When two mics at different
distances from a source are mixed together, every frequency will change in level by a different amount.
This makes for a very erratic (not flat) frequency
response.
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RECORDING DECEMBER 2016

Table of Contents for the Digital Edition of Recording - December 2016